Question: Simplify the following expression: $q = \dfrac{-36y^2 - 12y}{-12y^2 - 4y}$ You can assume $y \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-36y^2 - 12y = - (2\cdot2\cdot3\cdot3 \cdot y \cdot y) - (2\cdot2\cdot3 \cdot y)$ The denominator can be factored: $-12y^2 - 4y = - (2\cdot2\cdot3 \cdot y \cdot y) - (2\cdot2 \cdot y)$ The greatest common factor of all the terms is $4y$ Factoring out $4y$ gives us: $q = \dfrac{(4y)(-9y - 3)}{(4y)(-3y - 1)}$ Dividing both the numerator and denominator by $4y$ gives: $q = \dfrac{-9y - 3}{-3y - 1}$